Model complexity is widely used to provide a metric to make optimization traceable.
For example, a measure metric of the effective model complexity of neural networks helps to monitor the changes of a model during the optimization process and understand how the optimization process progresses [1]}, [2]}, [3]}, [4]}. Such a metric also helps to verify the effectiveness of new improvements of optimization algorithms [5]}. For example, Nakkiran et al. [4]} investigate the double descent phenomenon during training using effective complexity measured by the maximal size of the dataset on which zero training error can be achieved. They show that the double descent phenomenon can be represented as a function of the effective complexity. Raghu et al. [3]} and Hu et al. [2]} propose new regularization methods and demonstrate the effectiveness of these regularizations through their impact on complexity.
